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106-20083-MT1 - PROBLEM(1{25 pOlHIS Positixe charge Q is...

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Unformatted text preview: PROBLEM (1) {25 pOlHIS) Positixe charge Q is distributed nniftn’ml). around a I semicircle Ol‘ radius‘ R, as s'nuwn in the figure. Express your . ¥ Y B u answers in terms m“ some or all of the given quantities. related constants and unit vectors as needed (a) ([0 p13) Find the electric field at P. the center of the semicircle. Divide, The. fa’lwiifllifcjfiw mix-l0 mqll ElCu-Jln‘l'} l age, . Q 119 : ~ 6" t d :—‘—F~;e".vn‘r—-' -l [in Q IA S Tffi TT ' .l“'fln; aim—l x gE:L=~al:l—r,\'32é l k7“ // m- m2.“- (SQ \‘T Ems I516; : 53 (5M fij-Hil’fi) ,w T'l éyaf'altzj :folE wa:j¥flfh§ I'M: 33' (b) (7' pts) When a point charge q is placed at point A with coordinates (G, a), the net electric field at P becomes zero Find q. . . wmiuzmvym mama»; Dm M , : e! ugliest a}: i- l in“ um i 5 w ! 33M 59 a : é; em mi 95> imam f w, a»: w, l l+EL 0 "'"v‘ 543MB! : Phys 106 First Midterm Examénaticn Page 3 Saturday, July 1.8, 2009 PROBLEM [2} (35 points) The figiirc shows (ill electric tiipolc (with charge W; and fi. and H l 0 +5 l ” separation 11) in a uniform electric field between two xery large pzirnllcl GS I C} l__\, ,i‘ , t“ I , A, A (ind vertical plates. llizz platcs (NC at 'iislance 4d apart llie plates (in: A {J ‘* "in “I [ ‘—-— ,,,,,, r A l I. I insulating‘ and have uniform surface charge (lcnsmcs +Uand --0'. Both ' ,«\ 45° . | .1 ~ i -------- charges of the dipole he in the plant: ol the page. Express your answers wt} in terms of some or all of tho given quantities. related constants and E: J g E 5‘ 3' “rid—ma}t unit -'ectors as needed. ’ here is no gravity between the plates. {3) (5 pts) Using Gauss's law‘ find the electric field between the plates without the electric dipole. Express your answer in unit VCCIOI'S. ~ 4 .' ”1.. i"" tat . .- St-a 1:.»4 ‘-w 1' ‘-i“ SElQCi a ’35 Thai Ln") 6‘! Ckfliitiiéqj" Ami iirig "(3‘13 0‘ Pm F’li A i ““E P :3 it, «W14. 6“»! if 4. UL K ’3 g; i :3; i a J; i “*1 '3 ' if: 91..“ m \ $5M a l l?“ i P15“; F “1" 53 “g é {a "9",; g \r'} {Vfimt m 0‘ Jig: “i" 3‘; mL'EL‘E‘A' Wlw‘ém’jé‘ 2;}: “‘3'": "m _" "YR hi! i ..- :11 g! A l , M ~42 w ‘ i p ,3 Q. I? . i i it?“ Q ‘L A A (d) (10 pts) Find the work you must do to rotate the dipole from its given position to a vertical position so that the dipole moment is in the +yrdirection. ‘ ,L t i} w :1 ”31,1 WM 6 {a} AL-ai {13’ 3 5,4 % ,E V‘ _ q .5:- i .3 u , U‘ l W“W‘:f:‘;;: ' f L l W 2: iii—w: it “i? . "‘ a“ t, is w; as lwwwgiigw An = “Ii 51”“"73"1’”¢ uéw :1 mm” 1flC my“ L'If/Jtnrnw Cvfiminl‘ir‘inn Darin A thiirrlnv llilv l8, ?00q PROBLEM {3} (25 points) An inl‘initcly long cylindrical shell of inner radius a and outer radius :5 has a uniform Volume charge denSity ,0. A line of charge density P. is placed along the axis of the shell. 'l‘ake r as the distance From the axis. Express your answers in terms of some or all of the given quantitica related constants and unit vectors as needed. (a) (5 pts’) Find the electric field (magnitude and direction) for 0 < r < a. i aeieei a 6;; twat a; a “fir-mywin; ‘ 143"?” it“ 545* ':-- E; Pfit’iui” 1m rgqrefingl i ii flame; Car/rho? w'i‘i‘u The: shell ‘ $65152:[BLMMH T" a l .. h 42 E (2713”,. g, )2 ' ”Em Cog? (b) (7 pts) Find the electric field {magnitude and direction) for a < r <19. SQEQUE ”2 G3 9;? Lu $161.1? wt {’64}; (girl? we» a. er» a; 2;. ée C” A :1. Qfitml ! t u ‘ {fie-kaz-JQM +:.=.~+-,g,-,(;a.5 ~WW~=QM<=§mwTi 32mm;- -.....v. \ififiJ‘ a". E, a 'W», Skygfifié‘f'fi‘géVg .r-t E (we 3 : WM “" E “1 rm...“ .3 I LWEY?W% t” G .‘ ' mam: . .‘ 9., _ l (c) (8 pig) 1 ind [L16 electlic fie d (mannitude and direction) fori > b .................................................................. l [ If =._.na.gru- -Mwm“fl -s"-WV‘1-m“fimiifl‘rfin.kfifigd‘m‘fifiwmfllw ,getj a JS aeg tu pm'flnfigbu‘t web" adamr‘ighuguxg H” ' 5.5.5.;me v; we: “lat-‘9. .f fow’nrd f“ “A - I 4' €23 “M +1 A; (new; fig (d) (5 pts) Find the force {magnitude and direction) exerted or M “tori: _ the axis. F a ths l06 First Midterm Examination Page 5 95%,? "La—ug- ”mums. ,. a an electron by the electric field when it is placed at r : 219 from “’Mu-u‘w-‘(w-u + ”.1 (Lady) ‘5 ,__. , l_ . ' i .‘ Lfil'g’é: (Q) ) MCQ15 NIL-iflllfmu Saturday, July 18, 2009 PROBLEM (4) (35 points) A solid insuicitiiig sphere with radius is has a total positiw Chaigc +Q d isiiibiiied Ur. ifoimly thrigoi “iJIOLI it The, sphme [8 inside a contcmric conducting spherical shell with inner . G radius i’) and outer radius c. The spherical shelf has excess Charge +2Q. Take 1": 0 at infinity (r : Cr”-). (8) (6 p15} Find the pmential Vat r : (3 and r :f)(21tth<:0ut€r and inner surfaces of'tiie sphericai shcii. respectively). (a: 1’ ' . \‘4 m ‘1 F“ g“: “‘9 {A . _ ! “n H: a J t“ - cu m a C: amt. {5 an: a: v a“ r.“- s-g i l GE, ‘5" ESP if, \‘ j ,3 If“ a" .1", ‘ I '3” L, r" Q 2, ’1'” » {=1 0:: an r I) Q I .,"I an 2’ 8* r \ v «w 2. fan. ‘61“ a: 5.9:. .1..- m IQ 03‘ a. j (A ,1; 5 C (b) (7 pm) Find the potential V an =51§3tthe surface ofthe solid insuiating sphere) ---------------------------------------------- O (“5.3 L'} if. :3 fl ' “WWW!- fiéfi/xfiot jcmjcivn fr’rwjelwmfjmw QTJ-Jgfr‘g’f? ‘14.sz (“Law .f- f;‘; m‘ p I , c3. b 5:... a \ y ‘2 V‘LL—h‘flfl—‘L‘Rmm‘ _ i V91» ‘0 (/ 5G: (9: CS", + i) 4. ‘J {3% v *rW “WWW q” A) ”“1 k 1:. W q E“ g V fat; mafia Pg...“ . . z i 3m 9 28C $+~f~i+v . if? ””7757“ Writ... \{3 2. 3.62 an”: L. V? (J "— " E a ,s 1. aw“...,fl,...,.,...mmm..m,._w 9t a: \ '3’ ! iezgasg-igsmfiw ' c) (17 pts) Fmd 'he potential V at r w 0(at1he writer of [‘19 solid msuidtmg Sphprei ................................................ r) if 3' 5 Q 6“ iiécié, k (I ' ‘Lb‘ ‘ 7 J, 1* r" 1/”:- -""" “an. W ”K J ignvw;J.ggrmrJ(+ ([2.ri a~ Q a. .0) J {Am " .4 ' .2 G a a” h ‘5 I If“ ?‘ gagfi 7M, x ‘ JECPJAJ 5:0 I,“ L‘ finqflca-l 5f; 9‘}! ah 'ffid-—'—.3-{:? P :gég‘gqj b / rp in... I I ' s ‘ u 7 3“ wfl‘) J Jéu‘fiflfi “Nita, flag” 6‘2?! Ltfijffi. i 0‘3 a .. 3&2 i {érr)¢“2‘/;*W 599.5 ‘ .i “‘ :- , i G 335‘}. i t' '6 i. ‘ s. ,3 "F”. ":‘Mm I ’, t .. fiaw J" {(—69 (:7: .— 32 z“ e; i ‘ ’3 29x '2‘. ix .L. 4 ,2... “i. 4—- \ i 3/3"" “9(an A L? 6* / ‘ A . ‘ (Ln-I °“ f"? m A i 4‘90? .2“ ’3 C” I a -’ 3; Ly ,_ 1" '5 ‘5 ‘ I ”J. M... m. (A: _, h" m... ‘ --'~-—~-H-n~—~~'"‘“” 0 Q '9" r G i, V . fl 3L3c“2‘MQB+Q'C'L (1.7," . 2 v. " .. “U “m ‘ .. ‘15? fl.“ ’4 O i 9‘ U‘ :52- c. f t, _— F,“- q 3 2- -— “' (16‘. : Wr-"M-sn-“M-‘Wr-vm" u mus-“mm" """r““""' | Phys 106 First Midterm Examination Page 6 Saturday. Juiy 18,2009 ...
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